Use a transition matrix to predict the next step
A daily stock record classifies each item by its location
The matrix state order is warehouse and shop. Columns represent the current state and rows represent the state the next day. An entry is the proportion currently in its column state that will be in its row state the next day
\[T = \begin{bmatrix} 0.85 & 0.45 \\ 0.15 & 0.55 \end{bmatrix}\]
The current-state column uses the same state order. Its entries are counts of items
\[S_{\mathrm{now}} = \begin{bmatrix} 200 \\ 140 \end{bmatrix}\]